matrix_basis vs. matrix_local for object parented to bone
matrix_basis is simply a way to access the pose-bone or objects (location,scale,rotation) properties.

This is just for convenience - so you don't have to consider if euler/quaternion/axis-angle rotation are used when getting/setting a transformation.
matrix_local is the the objects world-space 4x4 matrix, relative to it's parent, if it has a parent - if the parent is a bone or a vertex, it will be relative to the parent matrix defined by the vertex/bone parent relationship.